Finite Group DatabasebetaFinite Group Databasebeta| order | 960 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C4 |
| direct product | C3×#65356 |
| Fitting | C3×C5×#125 ⋊ C2 |
| Hall | C3×C5 ⋊ #490 |
| Sylow | C5 ⋊ C3×#490 |
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,7,8,6)(9,11,12,16)(10,14,13,15)(17,18)(19,24)(20,22)(21,23);(9,10,12,13)(11,15,16,14)(18,22)(21,24);(5,6)(7,8)(10,13)(14,15)(18,21)(19,23)(22,24)132 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10598734, #14278356, C3×#10598735, … |
| maximal normal subgroup of | C3×#10598734, #14278356, C3×#10598735, … |
| maximal quotient of | C3×#10600341, C3×#10600410, C3×#10600346, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(960, 4159);